The transverse polarization of Lambda hyperons in e^+e^-rightarrow Lambda ^uparrow h X processes within TMD factorization

Abstract

We investigate the transverse polarization of the Lambda hyperon in the processes e^+e^-rightarrow Lambda ^uparrow pi ^pm X and e^+e^-rightarrow Lambda ^uparrow K^pm X within the framework of the transverse momentum dependent (TMD) factorization. The transverse polarization is contributed by the convolution of the transversely polarizing fragmentation function (PFF) D_{1T}^perp of the lambda hyperon and the unpolarized fragmentation function D_1 of pion/kaon. We adopt the spectator diquark model result for D_{1T}^{perp } to numerically estimate the transverse polarization in e^+e^-rightarrow Lambda ^uparrow h X process at the kinematical region of Belle Collaboration. To implement the TMD evolution formalism of the fragmentation functions, we apply two different parametrizations on the nonperturbative Sudakov form factors associated with the fragmentation functions of the Lambda , pion and kaon. It is found that our prediction on the polarization in the Lambda pi ^+ production and {bar{Lambda }} pi ^- is consistent with the recent Belle measurement in size and sign, while the model predictions on the polarizations in Lambda pi ^- and Lambda K^pm productions show strong disagreement with the Belle data. The reason for the discrepancies is discussed and possible approaches to improve the calculation in the future are also discussed.